Paper: Factorization of the hypergeometric-type difference equation on non-uniform lattices: dynamical algebra

Factorization of the hypergeometric-type difference equation on non-uniform lattices: dynamical algebra

Abstract

We argue that one can factorize the difference equation of hypergeometric type on the non-uniform lattices in general case. It is shown that in the most cases of q-linear spectrum of the eigenvalues this directly leads to the dynamical symmetry algebra suq(1,1), whose generators are explicitly constructed in terms of the difference operators, obtained in the process of factorization. Thus all models with the q-linear spectrum (some of them, but not all, previously considered in a number of publications) can be treated in a unified form.

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BibTeX

@article {MR2126099,
AUTHOR={\'{A}lvarez-Nodarse, R. and Atakishiyev, N. M. and Costas-Santos, R. S.},
TITLE={Factorization of the hypergeometric-type difference equation on non-uniform lattices: dynamical algebra},
JOURNAL={J. Phys. A},
FJOURNAL={Journal of Physics A. Mathematical and General},
VOLUME={38},
YEAR={2005},
NUMBER={1},
PAGES={153--174},
ISSN={0305-4470},
MRCLASS={39A13 (33D15)},
ZBL={1079.33017},
MRNUMBER={2126099},
MRREVIEWER={Lucia Di Vizio},
DOI={10.1088/0305-4470/38/1/011},
URL={https://doi.org/10.1088/0305-4470/38/1/011},
}